2001ApJ...549L..77W

The ultraluminous X-ray sources (ULXs) are unique in exhibiting moderately bright X-ray luminosities, L_X∼10³⁸-10⁴⁰ ergs.s^–1, and relatively high blackbody temperatures, T_in∼1.0-2.0 keV. From the constraint that L_X cannot exceed the Eddington luminosity L_E, we require relatively high black hole masses, M∼10-100 M_☉; however, for such large masses the standard disk theory predicts lower blackbody temperatures, T_in<1.0 keV. To understand a cause of this puzzling fact, we carefully calculate the accretion flow structure shining at ~L_E, fully taking into account the advective energy transport in the optically thick regime and the transonic nature of the flow. Our calculations show that at high accretion rate (M{dot}≳30L_E/c²) an apparently compact region with a size of R_in≃(1-3)r_g (with r_g being the Schwarzschild radius) is shining with a blackbody temperature of T_in≃1.8(M/10 M_☉)^–1/4 keV even for the case of a nonrotating black hole. Furthermore, R_in decreases as M{dot} increases, contrary to the canonical belief that the inner edge of the disk is fixed at the radius of the marginally stable last circular orbit. Accordingly, the loci of a constant black hole mass on the H-R diagram (representing the relation between L_X and T_in both on the logarithmic scales) are not straight but bent toward the lower M-direction in the frame of the standard disk relation.

We also plot the ASCA data of some ULXs on the same H-R diagram, finding that they all fall on the regions with relatively high masses, M∼10-30 M_☉, and high accretion rates, M{dot}≳10L_E/c². Interestingly, IC 342 source 1, in particular, was observed to move along the constant M line (not constant R_in line) in our simulations. This provides firm evidence that at least some ULXs are shining at ≳L_E and contain black holes with M≃10-100 M_☉.